Generating all rooted trees

Matlab code to enumerate all possible trees on n nodes: I wrote this awhile ago when I needed to enumerate all possible trees that could be formed by a set of n nodes. There are n^(n-1) such trees. This code uses the fact that there is a bijection between these trees and Prufer sequences. Here is tree_enumeration.m, which is a skeleton file for running code on all possible trees, and here is the function for generating the next tree, get_next_tree.m.

Jason Corso and I have been awarded a DARPA D3M grant. Our project is called SPIDER: Subspace Primitives that are Interpretable and DivERse. We will be contributing machine learning software primitives for a system that helps domain experts perform a wide variety of automated data analysis on their datasets. The project has 24 teams and is already off to a great start — We look forward to final system developed by this team over the next few years!

Congratulations to postdoc Greg Ongie, whose excellent work on Variety Models for Matrix Completion has been accepted to ICML. We’re very excited about the potential applications and open problems that we posed in this work. Congratulations also to John Lipor, whose work on Active Subspace Clustering has also been accepted to ICML — I’ve spoken about this work before at the Simons Institute workshop on Interactive Learning. It achieves state of the art clustering error on several benchmark datasets using very few pairwise cluster queries.

We also just finished a week at the SIAM Optimization conference, where our mini-symposium on Non-convex Optimization in Data Analysis was a huge hit. We had a full room for each session and 12 outstanding talks. Thanks to my co-organizers Stephen Wright, Rebecca Willett, and Rob Nowak, and thanks to all the speakers and participants.

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